Rational points on a subanalytic surface

Distribution of Rational Points: A Survey

Counting rational points on a certain exponential-algebraic surface

We study the distribution of rational points on a certain exponential-algebraic surface andwe prove, for this surface, a conjecture of A. J. Wilkie. 2000 Mathematics Subject Classification: 11G99, 03C64

The Density of Rational Points on Cayley ’ s Cubic Surface

The Cayley cubic surface is given by the equation 4 i=1 X −1 i = 0. We show that the number of non-trivial primitive integer points of size at most B is of exact order B(log B) 6 , as predicted by Manin's conjecture.

Rational Points on Quartics

Rational Points on Curves

This is an extended version of an invited lecture I gave at the Journées Arithmétiques in St. Étienne in July 2009. We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective) geometrically integral curve C over Q. The focus is on practical aspects of this problem in the case that the genus of C is at least 2, and therefore the set of rat...